Some Fine Properties of BV Functions on Wiener Spaces

Luigi Ambrosio; Michele Miranda Jr.; Diego Pallara

Analysis and Geometry in Metric Spaces (2015)

  • Volume: 3, Issue: 1, page 212-230, electronic only
  • ISSN: 2299-3274

Abstract

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In this paper we define jump set and approximate limits for BV functions on Wiener spaces and show that the weak gradient admits a decomposition similar to the finite dimensional case. We also define the SBV class of functions of special bounded variation and give a characterisation of SBV via a chain rule and a closure theorem. We also provide a characterisation of BV functions in terms of the short-time behaviour of the Ornstein-Uhlenbeck semigroup following an approach due to Ledoux.

How to cite

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Luigi Ambrosio, Michele Miranda Jr., and Diego Pallara. "Some Fine Properties of BV Functions on Wiener Spaces." Analysis and Geometry in Metric Spaces 3.1 (2015): 212-230, electronic only. <http://eudml.org/doc/271753>.

@article{LuigiAmbrosio2015,
abstract = {In this paper we define jump set and approximate limits for BV functions on Wiener spaces and show that the weak gradient admits a decomposition similar to the finite dimensional case. We also define the SBV class of functions of special bounded variation and give a characterisation of SBV via a chain rule and a closure theorem. We also provide a characterisation of BV functions in terms of the short-time behaviour of the Ornstein-Uhlenbeck semigroup following an approach due to Ledoux.},
author = {Luigi Ambrosio, Michele Miranda Jr., Diego Pallara},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {Wiener space; functions of bounded variation},
language = {eng},
number = {1},
pages = {212-230, electronic only},
title = {Some Fine Properties of BV Functions on Wiener Spaces},
url = {http://eudml.org/doc/271753},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Luigi Ambrosio
AU - Michele Miranda Jr.
AU - Diego Pallara
TI - Some Fine Properties of BV Functions on Wiener Spaces
JO - Analysis and Geometry in Metric Spaces
PY - 2015
VL - 3
IS - 1
SP - 212
EP - 230, electronic only
AB - In this paper we define jump set and approximate limits for BV functions on Wiener spaces and show that the weak gradient admits a decomposition similar to the finite dimensional case. We also define the SBV class of functions of special bounded variation and give a characterisation of SBV via a chain rule and a closure theorem. We also provide a characterisation of BV functions in terms of the short-time behaviour of the Ornstein-Uhlenbeck semigroup following an approach due to Ledoux.
LA - eng
KW - Wiener space; functions of bounded variation
UR - http://eudml.org/doc/271753
ER -

References

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